Atlas2,037 of 3,942

II.C.108

m₃ = 0.5

From Li & Liao (2017)

II.C.108 m₃ = 0.5 is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1 : 0.5 that return to their starting positions and velocities every 103.51 time units, published by Li & Liao (2017). The largest class in the atlas: hundreds of II.C orbits for seven mass ratios. It is unstable (largest Floquet multiplier 106), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000264 of each other at a top speed of 71.1, line up 144 times a period, and the computed loop closes to 3.5×10⁻²⁴.

Measured over one period

Period: 103.5125198
Masses: 1 : 1 : 0.5
Energy: -1.05963
Angular momentum: 0
Closest approach: 2.6×10⁻⁴
Top speed: 71.11
Path length: 254.93
Alignments per period: 144
Topology: aaBAbaBAbabABabAAbaBAbabABabABabAAbaBAbabABabABabAAbaBAbabABabAAbaBAbaBABabABaaBAbaBAbaBABabAB (free-group class)
Stability: unstable (|λ|max 106.0)
Loop closure: 3.5×10⁻²⁴

Neighbours on the map

All II.C orbits, the families of periodic three-body orbits, or the atlas map.